The title does allude to the three wise men from the Bible, kings that come from far away to bring the Christ child gold, frankincense, and myrrh: expensive and precious gifts to honor him. However, at the end of the story, the narrator says of Jim and Della, "Of all who give and receive gifts, such as they are the most wise. Everywhere they are the wise ones. They are the magi." Therefore, the title of the story doesn't simply allude to the original magi; the title actually refers to Jim and Della Young because they are the magi.
The narrator calls them the "most wise" because they understand that nothing in the world is as valuable as love. They both sacrifice the thing they own that is most important to them to show their love for the other: Jim sells his beautiful watch to buy Della hair combs, and Della sells her hair to buy Jim a watch chain. Their gifts require sacrifice, and the gifts given by the three rich kings did not: that makes Jim and Della the real magi.